Price gouging is an aspect of capitalism. Demand goes up, price goes up. Without market interference, this should force demand down.
Health care can't be forced down by price (at least, life saving health care), so you either have to stop providing care to those that need it but can't pay, or pass along the costs to others.
Health care costs can be forced down. The supply of doctors, nurses and other health professionals can be greatly increased (with free medical education or immigration, for example). Medicines can be mass produced by walking around (or over) copyrights and patents. Increasing competition (making it easier to switch provider, building more hospitals and facilities, etc. All these approaches have been tried, many of them are still working and result in lower costs without killing everyone.
I'm not saying those approaches don't have flow on effects, because they do but they can be used to lower costs. Don't assume price cannot be controlled by governments or industry, because it can be, and is.
Health care can't be forced down by price (at least, life saving health care), so you either have to stop providing care to those that need it but can't pay, or pass along the costs to others.